Kolata further confuses means and medians

I attack Gina Kolata's column below, and now she has published a defense in the NY Times to all the criticism. She still defends Prof. Gale, and writes:

For the unconvinced, Dr. Gale’s response:

What I did was to get a copy of the C.D.C. report and use the data in its tables. The C.D.C. groups people into four groups and gives percentage of men and women in each group



From these figures you can estimate the total partners claimed by each sex. I got between 40 percent and 75 percent more male than female partners depending on how you guess the average on each interval. Thus, the raw data is inconsistent (so it doesn’t matter whether you take averages or medians or any other statistic).

Yes, it does matter. If you assume that the men in these groups have 1, 3, 8, and 15 partners, while the women have 1, 5, 13, and 21 partners, then the women have slightly more partners than the men. The CDC data, as reported in the above table, is consistent. The men and women can have the same number of total partners, and yet the men have a median of 7 partners and the women have a median of 4 partners.

Prof. Gale is a very smart guy, and Kolata is one of the better science writers around, but this explanation is nonsense. It will only generate more email.

You can find additional comments on Slate and on this blog.

Here is more on why Kolata and the NY Times don't like to explain math properly.